# Power: energy transfer per time, without mass displacement?

1. Oct 31, 2015

The classical definition of power is the rate of work per unit time, and the usual definition of work requires a mass to be displaced. However, power is alternatively stated as the rate of the transfer of energy. Now, suppose for example that one abstractly considers a light beam (without measuring it). Energy is being transferred in space without any massive object being displaced. So can we talk about the power of the photon?
Thanks.

2. Oct 31, 2015

### Staff: Mentor

The way you described the photon does not suggest a way to use power to describe it. Photons have energy, but to get power from energy, you need time. So that would need to be something like photons per second (at a given energy).

3. Oct 31, 2015

OK, let me expand my description. Let us consider a field over an interval of time and a volume of space. There may be energy transfer without massive particle displacement.

4. Oct 31, 2015

### Chandra Prayaga

Moving a mass is only one way of doing work, or giving energy to a system. There are plenty of examples where other forms of energy exist, such as electric energy. A battery which drives a current through a circuit provides energy, and if that energy is provided over a certain time period, then the power is that energy divided by the time. No matter is being transported.

5. Oct 31, 2015

### nasu

6. Oct 31, 2015

### Staff: Mentor

Electrical power is voltage times current. Is that what you are thinking of?

Edit: we also transmit power wirelessly as in a radio transmitter and receiver.

7. Oct 31, 2015

Thank you, Chandra Prayaga, nasu and anorlunda. Chandra Prayaga and anorlunda are talking about electrical power, which transmits energy by the displacement of electrically charged particles, which are massive (which, again, goes back to the definition supplied by nasu, which talks of power in terms of energy being used; i.e., to move a (massive) body. ) For example, when we talk of transmitting power wirelessly, we are considering not only the photons moving between transmitter and receiver, but also the actions at the transmitter and receiver, where electrons are being moved. This still does not answer my original question: if the energy is not translating a mass during a certain interval of time, can we still talk of power?
To be specific, I am unsure of four separate cases: (1) considering a photon which is neither absorbed or emitted in a given time interval, or (2) potential energy, or (3) the absorption or emission of a photon by an electron around an atom in which the atom does not move but the energy level of the electron changes (although I am not sure that this is possible -- one refers to the energy level change in chemical reactions, but don't the atoms move, even if a tiny amount, to conserve momentum?) or (4) a quantum state which is not measured but changed by a gate in a quantum computation.
Thanks again.

8. Nov 1, 2015

### Staff: Mentor

A photon has no rest mass. However, it does carry both energy and momentum. That is true no matter what test case you invent.

Also, the drift motion of electrons in electric circuits does not contribute significantly to the energy transferred. It is a common misconception to think of them as massive particles with significant kinetic energy.

9. Nov 1, 2015

Thank you, anorlunda. My impression is that you are saying that electric power is due to the movement of charge, not the movement of electrons, hence one can speak of power not necessarily from the point of kinetic energy. Correct? Also, that a free photon then is a similar case, so that the power is just the amount of energy per second that would pass a fixed point: no mass is involved. Am I following you?
My question arises from Wikipedia's definition of power as "the rate of doing work. It is equivalent to an amount of energy consumed per unit time" whereby work is (still Wiki) done by a force "when acting on a body" and "consumed" is assumed to mean absorption and/or emission. I know Wikipedia is not the best place to learn physics, but would you then disagree with Wikipedia's definitions?
Thank you for your comments; they are helping me to clarify these concepts.

10. Nov 1, 2015

### Staff: Mentor

A photon has energy $hf$. If one photon per second moves past, then the power is $hf/second$.

Edit: Wikipedia is correct. Work has units of energy. Power has units of energy/time. Think of work in foot pounds, and horsepower in foot pounds per second.

11. Nov 1, 2015

Thanks again, anorlunda. Your first two sentences
[besides the fact that I think more in Newton-metres than foot pounds (when is America going to change to the metric system?)] just because two quantities have the same units do not make them identical; work is not the same as energy. My point was that Wiki's definitions seem to imply that power is due to either work being done on a body (not simply energy being transferred in spacetime) or by absorption/emission, but your example of the change with respect to time of the electromagnetic field at a point does not fit either one of these. So either Wiki's definitions or my logic are incomplete.

12. Nov 1, 2015

### Staff: Mentor

13. Nov 1, 2015

### Staff: Mentor

Yes, this is what is described by the Poynting vector. It represents the density of power transferred from one location to another through the EM fields.

14. Nov 1, 2015